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RSolve and known indexed variables
*To*: mathgroup at smc.vnet.net
*Subject*: [mg72299] RSolve and known indexed variables
*From*: "Chris Chiasson" <chris at chiasson.name>
*Date*: Tue, 19 Dec 2006 06:35:20 -0500 (EST)
Here is an attempt to solve a recurrence relation for the moment[i] at
particular parts of a beam under constant shear. The index is i.
lever[i] stands for the length of a particular section of the beam.
I would specify the "initial" condition for the moment at index 1, but
I want to show a problem into which I've run.
RSolve[{moment[i+1]\[Equal]moment[i]+shear*lever@i,
moment[10]\[Equal]someMoment},{moment[i]},i]
{{moment[i] -> someMoment - Sum[shear*lever[K$35], {K$35, K$36, 9}] +
Sum[shear*lever[K$35], {K$35, K$36, -1 + i}]}}
Notice that the output includes two sums, both with an index of K$35.
However, the range of the sums start at K$36. K$36 has no value. From
looking at the output, I would guess that K$36 should have the value
10 (the index at which I gave the initial condition for the moment).
For now: I will try to work around this by specifying my own generated
parameter and then detecting the appropriate Sum structures to find
the variable to replace.
I have also run into a problem where RSolve returns the input and an
RSolve::deqx error message if the input has one of these "known
indexed variables", even though the problem is actually separable (the
second part of the separate computation is shown above):
RSolve[{moment[10] == someMoment, shear[10] == someShear, moment[1 +
i] == moment[i] + lever[i]*shear[i],
shear[1 + i] == shear[i]}, {shear[i], moment[i]}, i]
So, uh, do you have any suggestions for making Mathematica handle the
combined problem? Do you have any methods for making Mathematica not
produce the K$36 variable in the output?
Note: This is one of the few times I have ever attempted to use
RSolve, and probably the first time in more than a year. I could
easily be using it incorrectly.
Second note: From the help browser documentation, it appears RSolve
was moved into the kernel from RSolve.m beginning with version 5, so
anyone with a version 4.x could probably view a copy of the source
code that is probably quite similar to what the internal code now
uses. I lack such a copy.
--
http://chris.chiasson.name/
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